Method of estimating a radio frequency offset based on sequences of predefined symbols, and receiver implementing said method

ABSTRACT

The invention concerns a method for estimating an offset between a radio frequency used by a receiver to form a baseband signal from a radio signal segment received through a communication channel and a carrier frequency of the radio signal of the segment. The radio signal segment is produced by a transmitter from a block of modulating symbols including at least two sequences of predefined symbols separated by information symbols. It consists in generating a frequency offset estimate on the basis of at least two sequences of baseband signal samples corresponding to two sequences of the block predefined symbols.

[0001] The present invention relates to digital radio communications. Itis more especially concerned with estimating the frequency offsets whichmay exist between a radio frequency used by a receiver to demodulate asignal received and the carrier of this signal.

[0002] Such frequency offsets may be due to the slightly differentcharacteristics of the frequency synthesizers with which the transmitterand the receiver are equipped, or to the carrier frequency driftintroduced by the radio wave propagation channel, in particular due tothe Doppler effect.

[0003] In a high throughput transmission context, it is desired toeconomize on the bandwidth, hence the data transmitted are weaklyprotected by the channel coding processes. This is the case especiallyfor the EGPRS packet mode (“EDGE Global Packet Radio Service”, EDGEstanding for “Enhanced Data for GSM Evolution”) provided in order toenhance the second-generation cellular radio telephony systems of GSMtype (“Global System for Mobile communications”) and derivatives. Insuch cases, a frequency difference or offset, even a small one, givesrise to residual errors which are unacceptable insofar as they causeappreciable degradation of the reception performance. The higher thefrequency band, the greater is this degradation. It can be avoided byeliminating the frequency offset by estimation and correction.

[0004] A particular, non-limiting application of the invention is inburst mode radio communications systems with time-division multiplexingof the channels (TDMA, “Time Division Multiple Access”).

[0005] A TDMA radio signal burst is formed by modulating a transmissioncarrier by means of a digital signal block which usually comprises atraining sequence composed of predefined symbols, which the receiverutilizes in particular to estimate the response of the propagationchannel (operation referred to as channel probing). The time structureof the radio signal transmitted on the carrier is composed of successiveframes subdivided into timeslots. A communication channel is typicallyformed by allotting a given timeslot in each frame, each timeslot beingcapable of containing a burst.

[0006] The existing processes for estimating the frequency offset at thereceiver end generally use the samples of the baseband signal whichcorrespond to the training sequence. The estimations thus obtained forseveral bursts pertaining to the same communication channel are filteredin order to increase the signal-to-noise ratio.

[0007] However, in the example of the context of high throughput packetmode transmission, several mobile terminals can use the same timeslot,so that the receiver's signal processing module no longer maps thereceived bursts onto the various transmitters. Therefore, the filteringof the estimations over several bursts becomes difficult to achieve, anda solution operating burst-by-burst is necessary.

[0008] However, when the frequency offset is small, typically of theorder of about 100 hertz, the consideration of the samples correspondingto the training sequence is not sufficient to provide a reliableestimate for each individual burst (this is the reason why the aforesaidfiltering is generally performed). The estimation of the frequencyoffset relies on a measurement of the phase rotation caused by thisoffset over the duration of the training sequence. This phase rotationis small since the training sequence should not be too long to avoidpenalizing the bandwidth. Under these conditions, a consequence of thenoise affecting the measurement is that the variance of the estimator isrelatively high.

[0009] Another case where burst-by-burst estimation can be very usefulis that of frequency hopping TDMA systems in which the communicationfrequency changes from one burst to another.

[0010] EP-A-0 950 568 and U.S. Pat. No. 5,245,611 describe otherfrequency offset estimation processes based on feedback with the aid ofthe symbols estimated by the channel equalizer. These processes providemore reliable estimations than the aforesaid direct processes, but theyhave the drawback of high complexity and hence of considerable cost interms of digital processing capacity.

[0011] An object of the present invention is to propose a reliablefrequency offset estimator, which in particular is capable of providinggood estimations on the scale of a TDMA radio signal burst withoutrequiring feedback on the part of a channel equalizer.

[0012] The invention thus proposes a method of estimating a frequencyoffset between a radio frequency used by a receiver to form a basebandsignal from a radio signal segment received along a communicationchannel and a carrier frequency of the radio signal of the segment, theradio signal segment being produced by a transmitter from a block ofmodulating symbols including at least two sequences of predefinedsymbols separated by information symbols. Before applying anequalization processing to the baseband signal so as to estimate theinformation symbols, at least one parameter is generated for estimatingthe frequency offset on the basis of at least two sequences of samplesof the baseband signal corresponding to two sequences of predefinedsymbols of the block.

[0013] The signal utilized to estimate the frequency offset extends overa relatively large duration since it covers a certain number of samplesrepresenting information symbols in addition to the sequences ofpredefined symbols. The larger phase rotation due to the frequencyoffset over this duration reduces the variance of the estimation.

[0014] The method makes it possible to estimate the frequency offsetjointly with the estimation of the impulse response of the channel andthereafter to correct this offset, thus making it possible to probe thechannel once the correction has been introduced.

[0015] The method is applicable to any mode of radio transmission and ofchannel multiplexing.

[0016] In one embodiment, the communication channel is time divisionmultiplexed, a radio signal segment received then consisting of a radiosignal burst.

[0017] The parameter for estimating the frequency offset may begenerated to process each radio signal burst individually, hence themethod is well suited to the packet mode.

[0018] However, by virtue of the decrease in the variance, the methodalso makes it possible to improve the estimations made when the receiveris capable of identifying a set of radio signal segments successivelyreceived from a given transmitter along the communication channel, i.e.in particular when its signal processing module knows the burst-mobilecorrespondence (packet mode with knowledge of the origin of theprocessed bursts, or circuit mode) in a TDMA application. In this case,the receiver filters the parameters for estimating the frequency offsetsuccessively generated for the segments or bursts of the set, so as toproduce a smoothed estimation of the frequency offset, which it can useto process the radio signal of these segments.

[0019] In a particular embodiment of the method, where the basebandsignal received is sampled at a frequency equal to Q times the frequencyof the symbols of the block, Q being an integer equal to or greater than1, and where the block comprises N symbols with positions 0 to N−1, witha first sequence of K(1) predefined symbols beginning from the positionP(1), a start sequence of K(0) predefined symbols beginning from theposition 0 and an end sequence of K(2) predefined symbols beginning fromthe position P(2)=N−K(2), where K(0), K(1), K(2) and P(1) are integerssuch that K(0)≧0, K(2)≧0, K(0)+K(2)>0, K(1)>L and P(1)≧K(0), L being apredetermined positive integer, the baseband signal comprises a firstvector S₁ of QK(1)−L complex samples corresponding to the firstsequence, a start vector S₀ of QK(0) complex samples corresponding tothe start sequence and an end vector S₂ of QK(2) complex samplescorresponding to the end sequence.

[0020] The parameter {circumflex over (φ)} for estimating the frequencyoffset can then be obtained according to$\hat{\varphi} = {\frac{b}{a}\left( {1 - \sqrt{1 + \frac{2{ac}}{b^{2}}}} \right)\quad {,\quad}}$

[0021] with: $\begin{matrix}{a = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\quad \left( {{\sum\limits_{i = 1}^{{QK}{(0)}}\quad {\left( {i - k - {P(1)} - L} \right)^{2}\beta_{0}^{i,\quad k}}} + {\sum\limits_{i = 1}^{k - 1}{\quad \left( {i - k} \right)^{2}\beta_{1}^{i,\quad k}}} +} \right.}} \\\left. {\sum\limits_{i = 1}^{{QK}{(2)}}\quad {\left( {i - k + {P(2)} - {P(1)}} \right)^{2}\beta_{2}^{i,\quad k}}} \right) \\{b = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\quad \left( {{\sum\limits_{i = 1}^{{QK}{(0)}}\quad {\left( {i - k - {P(1)} - L} \right)\alpha_{0}^{i,\quad k}}} + {\sum\limits_{i = 1}^{k - 1}{\quad \left( {i - k} \right)\alpha_{1}^{i,\quad k}}} +} \right.}} \\\left. {\sum\limits_{i = 1}^{{QK}{(2)}}{\quad \left( {i - k + {P(2)} - {P(1)}} \right)^{2}\alpha_{2}^{i,k}}} \right) \\{c = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\quad \left( {{\sum\limits_{i = 1}^{{QK}{(0)}}\quad \beta_{0}^{i,k}} + {\sum\limits_{i = 1}^{k - 1}\quad \beta_{1}^{i,\quad k}} + {\sum\limits_{i = 1}^{{QK}{(2)}}\quad \beta_{2}^{i,k}}} \right)}}\end{matrix}$

[0022] where, for m=0, 1 or 2, α_(m) ^(i,k) et β_(m) ^(i,k) are realnumbers such thatR_(m)^(i, k)S₁^(k)S_(m)^(i*) = α_(m)^(i, k) + j  β_(m)^(i,  k),  R_(m)^(i, k)

[0023] R_(m) ^(i,k) is a predetermined complex coefficient, S_(m) ^(i)designates the i-th sample of the vector S_(m) and (.)* the complexconjugate.

[0024] Alternatively, the parameters for estimating the frequency offsetcan comprise the three coefficients a, b and c defined hereinabove.These coefficients can be filtered to obtain respective smoothedcoefficients {overscore (a)}, {overscore (b)} and {overscore (c)} as afunction of which a smoothed estimation is produced through a similarformula.

[0025] It should be noted that the aforesaid “first sequence” maypossibly be situated at the start of the block (K(0)=P(1)=0) or at theend of the block (K(2)=0, P(1)+K(1)=N).

[0026] Another aspect of the present invention relates to a radiocommunication receiver, adapted for receiving radio signal segmentsalong a communication channel, each segment being produced by atransmitter from a block of modulating symbols comprising at least twosequences of predefined symbols separated by information symbols. Thereceiver comprises a radio stage forming a baseband signal from eachradio signal segment received along the communication channel, means forestimating a frequency offset between a radio frequency used for asegment in the radio stage and a carrier frequency of the radio signalof said segment, and equalization means for processing the basebandsignal so as to estimate the information symbols. The means forestimating the frequency offset are arranged to generate at least oneparameter for estimating the frequency offset, upstream of theequalization means, on the basis of at least two sequences of samples ofthe baseband signal corresponding to two sequences of predefined symbolsof the block.

[0027] Other features and advantages of the present invention willbecome apparent in the description below of non-limiting exemplaryembodiments, with reference to appended drawings, in which:

[0028]FIG. 1 is a chart showing the structure of a block of digitalsymbols from which a GSM signal burst is constructed;

[0029]FIG. 2 is a schematic diagram of a receiver according to theinvention;

[0030] FIGS. 3 to 5 are schematic diagrams of three embodiments of anestimation module of the receiver of FIG. 2.

[0031] The general case is considered of a radio signal segmentgenerated by a transmitter from a block of N modulating symbols y₀, y₁,. . . , Y_(N−1) having discrete values, for example y_(i)=±1 (binarysymbols) or y_(i)=±1±j (quaternary symbols), etc. The block comprisesseveral sequences of a priori known symbols. In the notation used here,the block will be regarded as comprising:

[0032] a sequence of K(0)≧0 known bits y_(P(0)), . . . , y_(P(0)+K(0)−1)situated at the start of the block, i.e. P(0)=0;

[0033] a sequence of K(J)≧0 known bits y_(P(J)), . . . , y_(P(J)+K(J)−1)situated at the end of the block, i.e. P(J)+K(J)=N;

[0034] J−1 sequences of respectively K(1), . . . , K(J−1) known bits,commencing respectively at positions P(1), . . . , P(J−1), with J>0 (J>1if K(0)=0 or K(J)=0, and J>2 if K(0)=K(J)=0), and for 1≦m≦J, K(m)>0 andP(m)>P(m−1)+K(m−1), the known bits of sequence m being y_(P(m)), . . . ,y_(P(m)+K(m)−1).

[0035] Between these sequences, the block contains information symbols apriori unknown.

[0036] In the case of the traffic channels of the GSM system, the ETSI(European Telecommunications Standards Institute) specifications fix thefollowing parameters for a segment consisting of a burst transmitted ina TDMA timeslot: N=148, J=1, K(0)=K(2)=3, K(1)=26 and P(1)=61 (see FIG.1). The central sequence of 26 symbols is the training sequenceconventionally used by the receiver to synchronize itself and toestimate the impulse response of the channel. The two three-symbolsequences situated at the ends of the block (“tail symbols”) aresubstantially shorter than the training sequence and serve to fix theconditions at the boundaries of the trellis of the channel equalizer.The symbols are real (binary) in the case of GMSK (“Gaussian MinimumShift Keying”) modulation used in particular for the telephony service,and complex (8-ary) in the case of EDGE modulation. The symbols of thetraining sequence are identical (real) in the GMSK and EDGE cases.

[0037] It is further assumed that the receiver samples the basebandsignal received s_(n) at a sampling frequency f_(e) equal to Q times thefrequency of the symbols, with Q integer equal to or greater than 1, andthat the support of the impulse response of the channel (including theinter-symbol interference of the modulation) extends over the durationof L+1 samples (L≧0). The complex samples of this impulse response aredenoted r_(k) with r_(k)=0 for k<0 and k>L. The response is representedby a vector r=(r₀, r₁, . . . , r_(L))^(T) (the notation (.)^(T)designates transposition).

[0038] By taking account of the frequency offset εf₀ (f₀ designates thecarrier frequency and δ the offset expressed relative to f₀), the linearrepresentation of the synchronized and sampled signal received can bewritten in the form: $\begin{matrix}{s_{n} = {{^{j\quad n\quad \varphi}{\sum\limits_{k = 0}^{{QN} - 1}\quad {x_{k}r_{n - k}}}} + N_{n}}} & (1)\end{matrix}$

[0039] In expression (1), the x_(k)'s (0≦k<QN) designate the sampledsymbols of the block, i.e. x_(k)=y_(i) for 0≦i<N and iQ≦k<(i+1)Q, N_(n)represents Gaussian additive white noise and φ a normalized phaseincrement proportional to the frequency offset, defined byφ=2πδf₀/f_(s).

[0040] In certain cases, multiple reception is performed with the helpof one or more antennas so as to improve the performance by diversity.Typically, the samples emanating from several diversity paths aresynchronized and then summed. In such a case, the signal received s_(n)considered here, having the expression (1), can consist of the summedsamples.

[0041] One seeks to construct an estimator {circumflex over (φ)} of thephase increment φ, this amounting to estimating the frequency offset, byusing only the samples of the current segment and with the smallestpossible variance. This is possible if the number of samples involvedand the distance between the first and the last of these samples arelarge.

[0042] The phase rotation due to the frequency offset between the firstand last symbol of the training sequence is 25φin the case of GSMsystems and derivatives. In the presence of a small frequency offset,this rotation is so small that it becomes difficult to estimate: thevariance of the estimator increases dramatically, thereby worsening theperformance of the receiver. For example, for a 45 Hz offset, the phaserotation over the training sequence is 1.5° in GSM 900 (900 MHz band)and 3° in DCS 1800 (variant in a 1800 MHz band). Taking into account the“tail symbols” in accordance with the invention makes it possible tomeasure a phase rotation due to the frequency offset between the firstand the last symbol of 147φ, and hence to greatly decrease the varianceof the estimator. In the example of the 45 Hz offset, the rotation is8.8° in GSM 900 and 17.6° in DCS 1800.

[0043] We consider hereafter the non-limiting example of a TDMA type ofradio communication system, the segment considered being a bursttransmitted in a timeslot.

[0044] For 0≦k<QN+L, u(k) denotes the vector defined for a burst by:u(k)^(T)=(x_(k), x_(k−1), . . . , x_(k−L)), with x_(−L)= . . . =x⁻¹=0and x_(QN)= . . . =x_(QN+L−1)=0, and we define J+1 Toeplitz matricesM_(m) with L+1 columns, which depend only on the symbols known a priori:M₀ = [u(0),  u(1),  …  ,  u(QK(0) − 1)]^(T),  with  QK(0)  rows;  for  1 ≤ m < J : M_(m) =   [u(QP(m) + L)  , [u(QP(m) + L + 1)  ,  …    ,  u(QP(m) + QK(m) − 1)]^(T),  with  QK(m) − L  rows; M_(j) = [u(QP(J) + L)  ,  u(QP(J) + L + 1),  …  ,  u(QN + L − 1)]^(T),  with  QK(J)rows.

[0045] Moreover we define J+1 vectors S_(m) composed of the complexsamples of the baseband signal received which correspond to the knownsymbols:

[0046] S₀=(s₀, s₁, . . . , s_(QK(0)−1))^(T), of size QK(0);

[0047] for 1≦m<J: S_(m)=(s_(QP(m)+L), s_(QP(m)+L+1), . . . ,s_(QP(m)−1))^(T), of size

[0048] QK(m)−L;

[0049] S_(j)=(S_(QP(J)+L), s_(QP(J)+L+1), . . . , s_(QN+L−1))^(T) ofsize QK(J).

[0050] We note $\gamma = \left( \frac{{QN} + L - 1}{2} \right)$

[0051] and, for any integer Z, D_(Z)=diag[1, e^(jφ), e^(2jφ), . . . ,e^(j(Z−1)φ)], the diagonal square matrix of size Z×Z whose respectivediagonal terms are 1, e^(jφ), e^(2jφ), . . . , e^(j(Z−1))φ. For 0≦m≦J,we define diagonal matrices Φ_(m) and Δ_(m) as follows:Φ₀ = ^(−jγφ) ⋅ D_(QK(0))  and  Δ₀ = diag[−γ,   − γ + 1,  …  ,   −   γ + QK(0) − 1],  each  of  size  QK(0) × QK(0);  for  1 ≤ m < J : Φ_(m) = ^(j(−γ + QP(m) + L)φ) ⋅ D_(QK(m) − L  )  and  Δ_(m) = diag[−γ + QP(m) + L  ,   − γ + QP(m) + L + 1  ,  …    ,   − γ + QP(m) +   QK(m) − 1],  each  of  size(QK(m) − L) × (QK(m) − L); Φ_(J) = ^(j(−γ + QP(J) + L)φ) ⋅ D_(QK(J))Δ_(J) = diag[−γ + QP(J) + L,   − γ + QP(J) + L + 1,  …  ,   − γ + QN + L − 1]  ,  each  of  size  QK(J) × QK(J).  

[0052] By considering only the known symbols of the block, model (1)gives J+1 linear systems which may each be written, to within a phase,in matrix form:

S_(m)=Φ_(m)M_(m)r+N_(m)  (2)

[0053] where N_(m) is a vector of Gaussian noise.

[0054] The application of the least squares criterion to these J+1linear systems leads to the following relations (3) and (4), which aresatisfied by the estimation {circumflex over (r)} of the impulseresponse vector r and those {circumflex over (Φ)}_(m) of the matricesΦ_(m) dependent on the phase increment φ: $\begin{matrix}{{\left( {\sum\limits_{m = 0}^{J}\quad {M_{m}^{H}M_{m}}} \right)\hat{r}} = {\sum\limits_{m = 0}^{J}\quad {M_{m}^{H}{\hat{\Phi}}_{m}^{H}S_{m}}}} & (3) \\{{\sum\limits_{m = 0}^{J}\quad \left( {{S_{m}^{H}{\hat{\Phi}}_{m}\Delta_{m}M_{m}\hat{r}} - {{\hat{r}}^{H}M_{m}^{H}\Delta_{m}{\hat{\Phi}}_{m}^{H}S_{m}}} \right)} = 0} & (4)\end{matrix}$

[0055] where (.)^(H) represents the conjugate transpose. Relation (3)yields a {circumflex over (100 )}-dependent estimation {circumflex over(r)}: $\begin{matrix}{\hat{r} = {\left( {\sum\limits_{m = 0}^{J}\quad {M_{m}^{H}M_{m}}} \right)^{- 1}\left( {\sum\limits_{M = 0}^{J}\quad {M_{m}^{H}{\hat{\Phi}}_{m}^{H}S_{m}}} \right)}} & (5)\end{matrix}$

[0056] which, fed back into relation (4), leads to: $\begin{matrix}{{\sum\limits_{m = 0}^{J}\quad \left\lbrack {{S_{m}^{H}{\hat{\Phi}}_{m}R_{m,\quad m}{\hat{\Phi}}_{m}^{H}S_{m}} + {2{j \cdot {lm}}\left\{ {\sum\limits_{p = {m + 1}}^{J}\quad {S_{m}^{H}{\hat{\Phi}}_{m}R_{m,\quad p}{\hat{\Phi}}_{p}^{H}S_{p}}} \right\}}} \right\rbrack} = 0} & (6)\end{matrix}$

[0057] where Im{.} represents the imaginary part of a complex number.The J(J+1)/2 matrices R_(m.p) of relation (6), given byR_(m,p)=Δ_(m)M_(m)PM_(p) ^(H)−M_(m)P^(H)M^(p) ^(H)Δ_(p) with${P = \left( {\sum\limits_{m = 0}^{J}{M_{m}^{H}M_{m}}} \right)^{- 1}},$

[0058] may be calculated once for all and stored by the receiver for0≦m≦p≦j.

[0059] An optimal estimator {circumflex over (φ)} for the current burstcan be calculated by the receiver by searching for a zero of relation(6) after having acquired the samples of the vectors S_(m). Of course,the more correct the synchronization of the receiver, i.e. the more themost important echoes of the channel have been included, the morereliable this estimator will be.

[0060] The above optimal estimator uses a channel probing performed onthe basis of the set of a priori known sequences. When a burst comprisesa single training sequence (J−1=1) and one or two short sequences of“tail symbols” at the start and at the end of the block, a less complexsolution consists in probing the channel on the basis of the trainingsequence alone. This solution is only slightly suboptimal since thesamples of the vectors S₀ and S₂ relating to the “tail symbols”, whichare relatively few in number, do not enhance the probing statisticsmuch, while they appreciably decrease the variance of the estimator ofthe phase increment, given that they span the entire length of theburst.

[0061] This last solution consists in making the following approximationin relation (5): $\begin{matrix}{\hat{r} = {\left( {M_{1}^{H}M_{1}} \right)^{- 1}M_{1}^{H}{\hat{\Phi}}_{1}^{H}S_{1}}} & (7)\end{matrix}$

[0062] The estimation according to the least squares criterion thengives: $\begin{matrix}{{{2{j \cdot {Im}}\left\{ {{S_{0}^{H}{\hat{\Phi}}_{0}R_{0}{\hat{\Phi}}_{1}^{H}S_{1}} + {S_{2}^{H}{\hat{\Phi}}_{2}R_{2}{\hat{\Phi}}_{1}^{H}S_{1}}} \right\}} + {S_{1}^{H}{\hat{\Phi}}_{1}R_{1}{\hat{\Phi}}_{1}^{H}S_{1}}} = 0} & (8)\end{matrix}$

[0063] where: R₁=Δ₁P′−P′Δ₁, of size [QK(1)−L]×[QK(1)−L], with Id theidentity matrix of rank L+1, and $\begin{matrix}{{P^{\prime} = {{M_{1}\left( {M_{1}^{H}M_{1}} \right)}^{- 1}\left( {{M_{0}^{H}M_{0}} + {M_{2}^{H}M_{2}} - {Id}} \right)\left( {M_{1}^{H}M_{1}} \right)^{- 1}M_{1}^{H}}};} \\{R_{m} = {{{{M_{m}\left( {M_{1}^{H}M_{1}} \right)}^{- 1}M_{1}^{H}\Delta_{1}} - {\Delta_{m}{M_{m}\left( {M_{1}^{H}M_{1}} \right)}^{- 1}M_{1}^{H}\quad {for}\quad m}} =}} \\{{{0\quad {and}\quad 2},{{of}\quad {size}\quad {{QK}(m)} \times {\left\lbrack {{{QK}(1)} - L} \right\rbrack.}}}}\end{matrix}$

[0064] By observing that the diagonal terms of the matrix R₁ are allzero and that R₁=−R₁ ^(H), relation (8) simplifies: $\begin{matrix}{{\sum\limits_{k = 1}^{{{QK}{(1)}} - L}{{Im}\left\{ {S_{1}^{k}{^{{- j}\quad k\quad \hat{\varphi}}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}{R_{0}^{i,k}S_{0}^{i^{*}}^{{j{({i - L})}}\hat{\varphi}}}} + {\sum\limits_{i = 1}^{k - 1}{R_{1}^{i,k}S_{1}^{i^{*}}^{{j{({{P{(1)}} + i})}}\hat{\varphi}}}} + {\sum\limits_{i = 1}^{{QK}{(2)}}{R_{2}^{i,k}S_{2}^{i^{*}}^{{j{({{P{(2)}} + i})}}\hat{\varphi}}}}} \right)}} \right\}}} = 0} & (9)\end{matrix}$

[0065] where R_(m) ^(i,k) designates the term situated in the i-th rowand k-th column of the matrix R_(m) (°≦M≦2), and S_(m) ^(i) the i-thcomponent of the vector S_(m) (S_(m) ^(i)=s_(i−1+P(m))) The R_(m) ^(i,k)are fixed coefficients calculated in advance, while the S_(m) ^(i) areacquired on receipt of the signal.

[0066] Equations (6) and (9) are nonlinear in {circumflex over (φ)} andpossess several roots. The correct root is the one closest to zero.Equation (6) or (9) can be solved by several interactive processes forsearching for roots of trigonometric polynomials. In practice, thepossible frequency offsets are fairly small (less than 270 Hz in thecase of GSM), so that the normalized phase increment φ is always verysmall compared with 1, thereby justifying the second-order approximatione^(jα{circumflex over (φ)})≈1+jα{circumflex over (φ)}−α²{circumflex over(φ)}²/2, giving rise to an estimate which can be easily calculateddirectly: $\begin{matrix}{\hat{\varphi} = {\frac{b}{a}\left( {1 - \sqrt{1 + \frac{2a\quad c}{b^{2}}}}\quad \right)}} & (10)\end{matrix}$

[0067] with, in the case of relation (9): $\begin{matrix}{a = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}{\left( {i - k - {P(1)} - L} \right)^{2}\beta_{0}^{i,k}}} + {\sum\limits_{i = 1}^{k - 1}{\left( {i - k} \right)^{2}\beta_{1}^{i,k}}} + {\sum\limits_{i = 1}^{{QK}{(2)}}{\left( {i - k + {P(2)} - {P(1)}} \right)^{2}\beta_{2}^{i,k}}}} \right)}} \\{b = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}{\left( {i - k - {P(1)} - L} \right)\alpha_{0}^{i,k}}} + {\sum\limits_{i = 1}^{k - 1}{\left( {i - k} \right)\alpha_{1}^{i,k}}} + {\sum\limits_{i = 1}^{{QK}{(2)}}{\left( {i - k + {P(2)} - {P(1)}} \right)^{2}\alpha_{2}^{i,k}}}} \right)}} \\{c = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}\beta_{0}^{i,k}} + {\sum\limits_{i = 1}^{k - 1}\beta_{1}^{i,k}} + {\sum\limits_{i = 1}^{{QK}{(2)}}\beta_{2}^{i,k}}} \right)}}\end{matrix}$

[0068] where α_(m) ^(i,k) and β_(m) ^(i,k) are the real numbers suchthatR_(m)^(i, k)S₁^(k)S_(m)^(i^(*)) = α_(m)^(i, k) + j  β_(m)^(i, k).

[0069] Once the samples s_(n) corresponding to the known sequences ofthe symbol block of the received baseband signal are available, theα_(m) ^(i,k) and β_(m) ^(i,k), the coefficients a, b and c and then theestimation {circumflex over (φ)} of the phase increment, which isproportional to the frequency offset, can be calculated directly.

[0070] The receiver represented in FIG. 2, which can in particular be aGSM receiver (mobile station or base station), comprises an antenna 1picking up a radio signal submitted to a radio reception stagecomprising an amplifier 2, a bandpass filter 3 and two mixers 4receiving the amplified and filtered radio signal. A local oscillator 5delivers two quadrature radio waves at the frequency of thecommunication channel employed by the receiver. The mixers 4 multiplythese two waves by the amplified and filtered radio signal, and theresulting signals are provided to low-pass filters 6 and then toanalog/digital converters 7 operating at the sampling frequency f_(e).The output signals from the converters 7 constitute the real andimaginary parts of the complex baseband signal s_(n).

[0071] This signal s_(n) may exhibit a phase drift if the frequency ofthe local oscillator 5 does not correspond exactly to the carrier of theradio signal picked up. It is to correct this drift that the estimatorof the frequency offset is used.

[0072] The estimation of the phase increment φ is performed by a module8, for example by using relation (10) above. Alternatively, the module 8can operate by applying an iterative calculation process.

[0073] The module 8 delivers the estimation {circumflex over (φ)},obtained for example according to relation (10), for each signal burstwith a view to the equalization processing applied to this burst by thechannel equalizer 9. A complex multiplier 10 corrects the samples s_(n)of the burst at the input of the equalizer 9 by multiplying them by thecomplex number e^(−jn{circumflex over (φ)}) (provided by the module 8(correction of the exponential term of relation (1)).

[0074] The estimation of the impulse response of the channel can beperformed on the basis of the corrected samples of the baseband signalor, as represented in FIG. 2, jointly with the estimation of thefrequency offset by the module 8. This estimation {circumflex over (r)}can be obtained by applying relation (5), where the matrix$\left( {\sum\limits_{m = 0}^{J}{M_{m}^{H}M_{m}}} \right)^{- 1}$

[0075] has been calculated once for all and stored in module 8, oraccording to relation (7), where the matrix (M₁ ^(H)M₁)⁻¹ M₁ ^(H) hasbeen calculated once for all and stored in module 8.

[0076] The equalizer 9 can thereafter, in a conventional manner,estimate the symbols ŷ_(n) of the block corresponding to the burst, withthe aid of the corrected samples and of the estimation {circumflex over(r)}.

[0077] With reference to FIGS. 3 to 5, the coefficients a, b and c offormula (10) are calculated for the current burst from the complexsignal s_(n), by way of the quantities α_(m) ^(i,k) and β_(m) ^(i,k), bycalculation modules 11, 12 belonging to the phase increment estimationmodule 8.

[0078] In the embodiments according to FIGS. 3 and 4, a module 13calculates the estimation {circumflex over (φ)} relating to the currentburst by applying formula (10).

[0079] In the case of FIG. 3, the estimation and the correction areperformed individually for the various bursts. A module 14 calculatesfor the various samples n of the current burst the corrective termse^(−jn{circumflex over (φ)}) provided to the multiplier 10, while theresponse r of the channel is estimated according to relation (7) by themodule 15.

[0080] In the embodiments according to FIGS. 4 and 5, a module 16 makesit possible to identify whether the current burst originates from agiven transmitter with which the receiver is communicating. This can beperformed by signaling, the timeslots alotted to each transmitterforming the subject of an allocation. A filtering of the parameters forestimating the frequency offset is effected by a module 17 to producetemporally smoothed parameters. The filtering consists for example of anaverage over a sliding or exponential window, applied to the burstsoriginating from one and the same transmitter.

[0081] In the case of FIG. 4, the parameter filtered by the module 17 isthe estimation {circumflex over (φ)} relating to the current burst,calculated by the module 13. The filtered estimation {circumflex over(φ)} produced by the module 17 is used by the modules 14 and 15 tocorrect the frequency offset and to estimate the channel.

[0082] In the case of FIG. 5, the parameters filtered by the module 17are the coefficients a, b and c relating to the current burst, which arecalculated by the module 12. The smoothed estimation {circumflex over(φ)}′ used by the modules 14 and 15 is obtained as a function of thesmoothed parameters {overscore (a)}, {overscore (b)}, {overscore (c)}according to the formula: $\begin{matrix}{{\hat{\varphi}}^{\prime} = {\frac{\overset{\_}{b}}{\overset{\_}{a}}\left( {1 - \sqrt{1 + \frac{2\overset{\_}{\quad {a\quad c}}}{{\overset{\_}{b}}^{2}}}} \right)}} & \left( 10^{\prime} \right)\end{matrix}$

1. A method of estimating a frequency offset between a radio frequencyused by a receiver to form a baseband signal (s_(n)) from a radio signalsegment received along a communication channel and a carrier frequencyof the radio signal of the segment, the radio signal segment beingproduced by a transmitter from a block of modulating symbols includingat least two sequences of predefined symbols separated by informationsymbols, characterized in that before applying an equalizationprocessing to the baseband signal so as to estimate the informationsymbols, at least one parameter ({circumflex over (φ)}; a, b, c) isgenerated for estimating the frequency offset on the basis of at leasttwo sequences of samples of the baseband signal (S_(m)) corresponding totwo sequences of predefined symbols of the block.
 2. The method asclaimed in claim 1, wherein the communication channel is time divisionmultiplexed, whereby a received radio signal segment consists of a radiosignal burst.
 3. The method as claimed in claim 2, wherein the parameter({circumflex over (φ)}) for estimating the frequency offset is generatedto process each radio signal burst individually.
 4. The method asclaimed in any one of the preceding claims, comprising the steps ofidentifying a set of radio signal segments successively received fromthe transmitter along the communication channel and intended for thereceiver, and filtering the parameters ({circumflex over (φ)}; a, b, c)for estimating the frequency offset successively generated for thesegments of the set to produce a smoothed estimation ({circumflex over(φ)}′) of the frequency offset, used to process the radio signal of thesegments of the set.
 5. The method as claimed in any one of thepreceding claims, wherein said sequences of predefined symbols comprisetwo sequences respectively situated at the start and at the end of theblock of modulating symbols.
 6. The method as claimed in any one of thepreceding claims, wherein said sequences of predefined symbols comprisea first sequence and at least one second sequence situated at an end ofthe block of modulating symbols and substantially shorter than the firstsequence.
 7. The method as claimed in claim 6, wherein the parameter({circumflex over (φ)}; a, b, c) for estimating the frequency offset isgenerated on the basis of the first sequence and of each secondsequence, while the response of the communication channel is estimatedon the basis of the first sequence alone.
 8. The method as claimed inany one of the preceding claims, wherein the baseband signal (s_(n)) issampled at a frequency equal to Q times the frequency of the symbols ofthe block, Q being an integer equal to or greater than 1, wherein theblock comprises N symbols with positions 0 to N−1, with a first sequenceof K(1) predefined symbols beginning from the position P(1), a startsequence of K(0) predefined symbols beginning from the position 0 and anend sequence of K(2) predefined symbols beginning from the positionP(2)=N−K(2), where K(0), K(1), K(2) and P(1) are integers such thatK(0)≧0, K(2)≧0, K(0)+K(2)>0, K(1)>L and P(1)≧K(0), L being apredetermined positive integer, wherein the baseband signal comprises afirst vector S₁ of QK(1)−L complex samples corresponding to the firstsequence, a start vector S₀ of QK(0) complex samples corresponding tothe start sequence and an end vector S₂ of QK(2) complex samplescorresponding to the end sequence, and wherein the parameter {circumflexover (φ)} for estimating the frequency offset is obtained according to${\hat{\varphi} = {\frac{b}{a}\left( {1 - \sqrt{1 + \frac{2\quad a\quad c}{b^{2}}}} \right)}},$

 with:$a = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}{\left( {i - k - {P(1)} - L} \right)^{2}\beta_{0}^{i,k}}} + {\underset{i = 1}{\overset{k - 1}{\sum\quad}}{\left( {i - k} \right)^{2}\beta_{1}^{i,k}{\sum\limits_{i = 1}^{{QK}{(2)}}{\left( {i - k + {P(2)} - {P(1)}} \right)^{2}\beta_{2}^{i,k}}}}}} \right)}$$b = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}{\left( {i - k - {P(1)} - L} \right)\alpha_{0}^{i,k}}} + {\underset{i = 1}{\overset{k - 1}{\sum\quad}}\left( {i - k} \right)\alpha_{1}^{i,k}{\sum\limits_{i = 1}^{{QK}{(2)}}{\left( {i - k + {P(2)} - {P(1)}} \right)^{2}\alpha_{2}^{i,k}}}}} \right)}$$c = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}\beta_{0}^{i,k}} + {\sum\limits_{i = 1}^{k - 1}\beta_{1}^{i,k}} + {\sum\limits_{i = 1}^{{QK}{(2)}}\beta_{2}^{i,k}}} \right)}$

 where, for m=0, 1 or 2, α_(m) ^(i,k) et β_(m) ^(i,k) are real numberssuch that R_(m) ^(i,k)S₁ ^(k)S_(m) ^(i*)=α_(m) ^(i,k)+jβ_(m) ^(i,k),R_(m) ^(i,k) is a predetermined complex coefficient, S_(m) ^(i)designates the i-th sample of the vector S_(m) and (.)* the complexconjugate.
 9. The method as claimed in any one of claims 1 to 7, whereinthe baseband signal (s_(n)) is sampled at a frequency equal to Q timesthe frequency of the symbols of the block, Q being an integer equal toor greater than 1, wherein the block comprises N symbols with positions0 to N−1, with a first sequence of K(1) predefined symbols beginningfrom the position P(1), a start sequence of K(0) predefined symbolsbeginning from the position 0 and an end sequence of K(2) predefinedsymbols beginning from the position P(2)=N−K(2), where K(0), K(1), K(2)and P(1) are integers such that K(0)≧0, K(2)≧0, K(0)+K(2)>0, K(1)>L andP(1)≧K(0), L being a predetermined positive integer, wherein thebaseband signal comprises a first vector S, of QK(1)−L complex samplescorresponding to the first sequence, a start vector S0 of QK(0) complexsamples corresponding to the start sequence and an end vector S₂ ofQK(2) complex samples corresponding to the end sequence, wherein theparameters for estimating the frequency offset comprise threecoefficients a, b and c given by:$a = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}{\left( {i - k - {P(1)} - L} \right)^{2}\beta_{0}^{i,k}}} + {\underset{i = 1}{\overset{k - 1}{\sum\quad}}{\left( {i - k} \right)^{2}\beta_{1}^{i,k}{\sum\limits_{i = 1}^{{QK}{(2)}}{\left( {i - k + {P(2)} - {P(1)}} \right)^{2}\beta_{2}^{i,k}}}}}} \right)}$$b = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}{\left( {i - k - {P(1)} - L} \right)\alpha_{0}^{i,k}}} + {\underset{i = 1}{\overset{k - 1}{\sum\quad}}\left( {i - k} \right)\alpha_{1}^{i,k}{\sum\limits_{i = 1}^{{QK}{(2)}}{\left( {i - k + {P(2)} - {P(1)}} \right)^{2}\alpha_{2}^{i,k}}}}} \right)}$$c = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}\beta_{0}^{i,k}} + {\sum\limits_{i = 1}^{k - 1}\beta_{1}^{i,k}} + {\sum\limits_{i = 1}^{{QK}{(2)}}\beta_{2}^{i,k}}} \right)}$

 where, for m=0, 1 or 2, α_(m) ^(i,k) et β_(m) ^(i,k) are real numberssuch thatR_(m)^(i, k)S₁^(k)S_(m)^(i^(*)) = α_(m)^(i, k) + jβ_(m)^(i, k), R_(m)^(i, k)

 is a predetermined complex coefficient, S_(m) ^(i) designates the i-thsample of the vector S_(m) and (.)* the complex conjugate, the methodcomprising the steps of identifying a set of radio signal segmentssuccessively received from the transmitter along the communicationchannel and intended for the receiver, and filtering the coefficients a,b and c to obtain respective smoothed coefficients {overscore (a)},{overscore (b)} and {overscore (c)} as a function of which is produced asmoothed estimation${\hat{\varphi}}^{\prime} = {\frac{\overset{\_}{b}}{\overset{\_}{a}}\left( {1 - \sqrt{1 + \frac{2\quad \overset{\_}{a\quad c}}{{\overset{\_}{b}}^{2}}}} \right)}$

 used to process the radio signal of the segments of the set.
 10. Aradio communication receiver, adapted for receiving radio signalsegments along a communication channel, each segment being produced by atransmitter from a block of modulating symbols comprising at least twosequences of predefined symbols separated by information symbols, thereceiver comprising a radio stage (2-7) forming a baseband signal(s_(n)) from each radio signal segment received along the communicationchannel, means (8) for estimating a frequency offset between a radiofrequency used for a segment in the radio stage and a carrier frequencyof the radio signal of said segment, and equalization means (9) forprocessing the baseband signal to estimate the information symbols,characterized in that the means for estimating the frequency offset arearranged to generate a parameter ({circumflex over (φ)}; a, b, c) forestimating the frequency offset, upstream of the equalization means, onthe basis of at least two sequences of samples of the baseband signalcorresponding to two sequences of predefined symbols of the block. 11.The receiver as claimed in claim 10, wherein the communication channelis time division multiplexed, whereby a radio signal segment receivedconsists of a radio signal burst.
 12. The receiver as claimed in claim11, further comprising means (9-10) for processing each radio signalburst by taking account of the parameter ({circumflex over (φ)}) forestimating the frequency offset generated individually for said burst bythe estimation means (8).
 13. The receiver as claimed in any one ofclaims 10 to 12, further comprising means (16) for identifying a set ofradio signal segments successively received from the transmitter alongthe communication channel and intended for the receiver, and means(9-10) for processing the radio signal of the segments of the set bytaking account of a smoothed estimation ({circumflex over (φ)}) of thefrequency offset produced by the estimation means (8) by filtering theparameters ({circumflex over (φ)}; a, b, c) for estimating the frequencyoffset successively generated for the segments of the set.
 14. Thereceiver as claimed in any one of claims 10 to 13, wherein saidsequences of predefined symbols comprise two sequences respectivelysituated at the start and at the end of the block of modulating symbols.15. The receiver as claimed in any of claims 10 to 14, wherein saidsequences of predefined symbols comprise a first sequence and at leastone second sequence situated at an end of the block of modulatingsymbols and substantially shorter than the first sequence.
 16. Thereceiver as claimed in claim 15, wherein the means (8) for estimatingthe frequency offset are arranged to generate the estimation of thefrequency offset on the basis of the first sequence and of each secondsequence, the receiver further comprising means (15) for estimating theresponse of the communication channel on the basis of the first sequencealone.
 17. The receiver as claimed in any one of claims 10 to 16,wherein the baseband signal (s_(n)) is sampled at a frequency equal to Qtimes the frequency of the symbols of the block, Q being an integerequal to or greater than 1, wherein the block comprises N symbols withpositions 0 to N−1, with a first sequence of K(1) predefined symbolsbeginning from the position P(1), a start sequence of K(0) predefinedsymbols beginning from the position 0 and an end sequence of K(2)predefined symbols beginning from the position P(2)=N−K(2), where K(0),K(1), K(2) and P(1) are integers such that K(0)≧0, K(2)≧0, K(0)+K(2)>0,K(1)>L and P(1)≧K(0), L being a predetermined positive integer, whereinthe baseband signal comprises a first vector S₁ of QK(1)−L complexsamples corresponding to the first sequence, a start vector S₀ of QK(0)complex samples corresponding to the start sequence and an end vector S₂of QK(2) complex samples corresponding to the end sequence, and whereinthe parameter {circumflex over (φ)} for estimating the frequency offsetis obtained by the estimation means (8) according to${\hat{\varphi} = {\frac{b}{a}\left( {1 - \sqrt{1 + \frac{2\quad a\quad c}{b^{2}}}} \right)}},$

 with:$a = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}{\left( {i - k - {P(1)} - L} \right)^{2}\beta_{0}^{i,k}}} + {\underset{i = 1}{\overset{k - 1}{\sum\quad}}{\left( {i - k} \right)^{2}\beta_{1}^{i,k}{\sum\limits_{i = 1}^{{QK}{(2)}}{\left( {i - k + {P(2)} - {P(1)}} \right)^{2}\beta_{2}^{i,k}}}}}} \right)}$$b = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}{\left( {i - k - {P(1)} - L} \right)\alpha_{0}^{i,k}}} + {\underset{i = 1}{\overset{k - 1}{\sum\quad}}\left( {i - k} \right)\alpha_{1}^{i,k}{\sum\limits_{i = 1}^{{QK}{(2)}}{\left( {i - k + {P(2)} - {P(1)}} \right)^{2}\alpha_{2}^{i,k}}}}} \right)}$$c = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}\beta_{0}^{i,k}} + {\sum\limits_{i = 1}^{k - 1}\beta_{1}^{i,k}} + {\sum\limits_{i = 1}^{{QK}{(2)}}\beta_{2}^{i,k}}} \right)}$

 where, for m=0, 1 or 2, α_(m) ^(i,k) et β_(m) ^(i,k) are real numberssuch thatR_(m)^(i, k)S₁^(k)S_(m)^(i^(*)) = α_(m)^(i, k) + jβ_(m)^(i, k), R_(m)^(i, k)

 is a predetermined complex coefficient, S_(m) ^(i) designates the i-thsample of the vector S_(m) and (.)* the complex conjugate.
 18. Thereceiver as claimed in any one of claims 10 to 16, wherein the basebandsignal (s_(n)) is sampled at a frequency equal to Q times the frequencyof the symbols of the block, Q being an integer equal to or greater than1, wherein the block comprises N symbols with positions 0 to N−1, with afirst sequence of K(1) predefined symbols beginning from the positionP(1), a start sequence of K(0) predefined symbols beginning from theposition 0 and an end sequence of K(2) predefined symbols beginning fromthe position P(2)=N−K(2), where K(0), K(1), K(2) and P(1) are integerssuch that K(0)≧0, K(2)≧0, K(0)+K(2)>0, K(1)≧L and P(1)≧K(0), L being apredetermined positive integer, wherein the baseband signal comprises afirst vector S₁ of QK(1)−L complex samples corresponding to the firstsequence, a start vector S₀ of QK(0) complex samples corresponding tothe start sequence and an end vector S₂ of QK(2) complex samplescorresponding to the end sequence, and wherein the parameters forestimating the frequency offset comprise three coefficients a, b and cobtained by the estimation means (8) according to:$a = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}{\left( {i - k - {P(1)} - L} \right)^{2}\beta_{0}^{i,k}}} + {\underset{i = 1}{\overset{k - 1}{\sum\quad}}{\left( {i - k} \right)^{2}\beta_{1}^{i,k}{\sum\limits_{i = 1}^{{QK}{(2)}}{\left( {i - k + {P(2)} - {P(1)}} \right)^{2}\beta_{2}^{i,k}}}}}} \right)}$$b = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}{\left( {i - k - {P(1)} - L} \right)\alpha_{0}^{i,k}}} + {\underset{i = 1}{\overset{k - 1}{\sum\quad}}\left( {i - k} \right)\alpha_{1}^{i,k}{\sum\limits_{i = 1}^{{QK}{(2)}}{\left( {i - k + {P(2)} - {P(1)}} \right)^{2}\alpha_{2}^{i,k}}}}} \right)}$$c = {\sum\limits_{k = 1}^{{{QK}{(1)}} - L}\left( {{\sum\limits_{i = 1}^{{QK}{(0)}}\beta_{0}^{i,k}} + {\sum\limits_{i = 1}^{k - 1}\beta_{1}^{i,k}} + {\sum\limits_{i = 1}^{{QK}{(2)}}\beta_{2}^{i,k}}} \right)}$

 where, for m=0, 1 or 2, α_(m) ^(i,k) et β_(m) ^(i,k) are real numberssuch thatR_(m)^(i, k)S₁^(k)S_(m)^(i^(*)) = α_(m)^(i, k) + jβ_(m)^(i, k), R_(m)^(i, k)

 is a predetermined complex coefficient, S_(m) ^(i) designates the i-thsample of the vector S_(m) and (.)* the complex conjugate, the receiverfurther comprising means (16) for identifying a set of radio signalsegments successively received from the transmitter along thecommunication channel and intended for the receiver and means (9-10) forprocessing the radio signal of the segments of the set by taking accountof a smoothed estimation${\hat{\varphi}}^{\prime} = {\frac{\overset{\_}{b}}{\overset{\_}{a}}\left( {1 - \sqrt{1 + \frac{2\overset{\_}{ac}}{{\overset{\_}{b}}^{2}}}} \right)}$

 of the frequency offset produced by the estimation means (8) as afunction of smoothed coefficients {overscore (a)}, {overscore (b)} and{overscore (c)} calculated by filtering the coefficients a, b and csuccessively obtained by the estimation means (8) for the segments ofthe set.